The aim of this paper is to promote web geometry and, especially, the Reidemeister closure condition as a powerful and intuitive tool characterizing associativity of the Archimedean triangular norms. In order to demonstrate its possible applications, we provide the full solution to the problem of convex combinations of nilpotent triangular norms. Keywords— Archimedean triangular norm, web geome...

We generalize a major portion of the classical theory of Cand C embedded subspaces to pointfree topology, where the corresponding notions are frame Cand C -quotients. The central results characterize these quotients and generalize Urysohn’s Extension Theorem, among others. The proofs require calculations in CL, the archimedean f -ring of frame maps from the topology of the reals into the frame ...

In [7], results about the global Jacquet-Langlands correspondence, (weak and strong) multiplicity-one theorems and the classification of automorphic representations for inner forms of the general linear group over a number field are established, under the condition that the local inner forms are split at archimedean places. In this paper, we extend the main local results of [7] to archimedean p...

1.1. Motivation. Over C and over non-archimedean fields, analytification of algebraic spaces is defined as the solution to a quotient problem. Such analytification is interesting, since in the proper case it beautifully explains the essentially algebraic nature of proper analytic spaces with “many” algebraically independent meromorphic functions. (See [A] for the complex-analytic case, and [C3]...

In this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-Archimedean number with $alpha^{-2}neq 3$. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the quadratic $alpha$-functional equation (0.1) in non-Archimedean Banach spaces.

Suppose <? denotes a class of totally ordered groups closed under taking subgroups and quotients by o-homomorphisms. We study the following classes: (1) Res (£?), the class of all lattice-ordered groups which are subdirect products of groups in C; (2) Hyp(C), the class of lattice-ordered groups in Res(C) having all their ¿-homomorphic images in Res(<?); Para(C), the class of lattice-ordered gro...

In the book Tilings and Patterns by B. Grunbaum and G. S. Shephard, the problem of classifying the uniform edge-c-colorings of Archimedean tilings of the Euclidean plane is posed. This article provides such a classification.

Given a dependent censored data (X, δ) = (min(T, C), I(T < C)) from an Archimedean copula model, we give general formulas for possible marginal survival functions of T and C. Based on our formulas, we can easily establish the relationship between all these survival functions and derive some useful identifiability results. Also based on our formulas, we propose a new estimator of the marginal su...

in an earlier work we showed that for ordered fields f not isomorphic to the reals r, there are continuous 1-1 unctions on [0, 1]f which map some interior point to a boundary point of the image (and so are not open). here we show that over closed bounded intervals in the rationals q as well as in all non-archimedean ordered fields of countable cofinality, there are uniformly continuous 1-1 func...

The Archimedean property is one of the most beautiful axioms of the classical arithmetic and some of the methods of constructing the field of real numbers are based on this property. It is well-known that every Archimedean `-group is abelian and every pseudo-MV algebra is commutative. The aim of this paper is to introduce the Archimedean property for pseudo-MTL algebras and FLw-algebras. The ma...